The problem with cell towers is that the infrastructure is more brittle with more moving parts. There's been cases where fires, power outages etc in small towns have caused base stations to go offline, cutting whole towns off from communication.
Not to mention the recent case where penetration testing done by another operator in Europe accidentally caused the entire cell phone network of the largest operator in Norway to go offline for half a day.
Edit: Adding generators/batteries to a significant fraction of cell towers is (probably) impractical due to them being bulky, expensive, and attractive to thieves.
Them being bulky is a major deterrent to theft, as a lot of our cellphone infrastructure is way out in the boonies and not really accessible unless you REALLY want to get to it...
It is my own phone batter. Or my spouse's - he has a dying phone with a dying battery, which doesn't always like to hold a charge. I'll be good for a while, sure, but once I'm dead... I'm dead. If something would happen late at night, after I've fiddled with my phone all day, I might start out with very little power. Early in the day, and I could make it last most the weekend.
Here's the FCC ruling: http://www.njslom.org/FCC-07-177A1.pdf (page 23)